Fibre optic communication systems are today present in all telecommunications networks, and carry more than 80% of the world's long-distance signals. The success of optical networks is based on the invention of low-loss silica-based optical fibres, known as single-mode fibres (SMFs). These have allowed successive system capacity upgrades to meet the exponentially-growing user demand while simultaneously reducing the cost per transported information bit. However, silica-based fibres experience a significant limitation, wherein the refractive index of the fibres varies nonlinearly in response to an applied electric field. As a result, a signal distortion is introduced which increases nonlinearly with the signal power. More specifically, the distortion increases faster (approximately quadratically) than the increase in signal power. As a result, there is a maximum quantity of information that can be transmitted over the low-loss frequency band in optical fibres. The capacity limit can be calculated using the Shannon-Hartley theorem modified to include fibre nonlinearities, as discussed in Ellis et al. (2010) [A. Ellis, J. Zhao, D. Cotter, “Approaching the Non-Linear Shannon Limit,” IEEE/OSA Journal of Lightwave Technology, vol. 28, no. 4, 2010].
Previously the Kerr effect has been addressed using nonlinearity compensation. Electronic compensation techniques are described in Ho et al. (2004) [K-P. Ho, and J. Kahn, “Electronic compensation technique to mitigate nonlinear phase noise,” IEEE/OSA Journal of Lightwave Technology, vol. 22, pp. 779-783, 2004] and Ip et al. (2008) [E. Ip, and J. Kahn, “Compensation of dispersion and nonlinear impairments using digital back propagation,” IEEE/OSA Journal of Lightwave Technology, vol. 26, pp. 3416-3425, 2008]. However, these present limitations such as the inability to mitigate interchannel nonlinear impairments, which require the knowledge of other wavelength-division multiplexing channels which may be unknown to the compensator, and the high complexity involved when many computation steps are required to undo nonlinear interactions in the case of dispersive transmission.
Mid-span spectral inversion (MSSI) is a well-known technique which is used to compensate chromatic dispersion, nonlinearity and the combined effect of the two. This is done by performing phase conjugation on the electric field of the optical signal near the middle of a transmission link and is described for example in Marcenac et al. (1997) and Jansen et al. (2006) [D. Marcenac, D. Nesset, A. Kelly, M. Brierley, A. Ellis, D. Moodie, C. Ford, “40 Gbit/s transmission over 406 km of NDSF using mid-span spectral inversion by four-wave-mixing in a 2 mm long semiconductor optical amplifier,” in Electronics Letters, vol. 33, no. 10, pp. 879-880, 1997; S. L. Jansen, D. Borne, B. Spinnler, S. Calabro, H. Suche, P. M. Krummrich, W. Sohler, G.-D. Khoe, and H. de Waardt, “Optical phase conjugation for ultra long-haul phase-shift-keyed transmission,” IEEE/OSA Journal of Lightwave Technology, vol. 24, pp. 54, 2006]. A transmission link using an MSSI method is shown in FIG. 2(a). However, MSSI requires that the transmission link be modified by inserting a phase conjugator inside the link, and requires symmetric power evolutions around the phase conjugator, leading to increased deployment requirements.
More recently, an alternative solution (herein: “the PCTW method”) has been proposed. The method involves the cancellation of nonlinear signal-to-signal interactions by transmitting a pair of mutually phase-conjugated twin-waves (PCTW) together through the orthogonal polarization modes of a single optical fibre and coherently superimposing them electronically at the receiver site. This is discussed in Liu et al. (2013) [X. Liu, A. Chraplyvy, P. Winzer, R. Tkach and S. Chandrasekhar, “Phase-conjugated twin waves for communication beyond the Kerr nonlinearity limit,” Nature Photonics, 2013]. There are several drawbacks to this method though, since half of the transmission capacity of every network element crossed is wasted to transmit the twin copy and the complexity of the receiver is increased, and more specifically, a coherent receiver is required. A schematic diagram of such a method is shown in FIG. 2(b).